My hinge simulation is not working correctly
From what I can tell, it appears that your setup has a number of issues (and please correct me if I am mistaken on anything here). The biggest one being that the physical design of the flaps and how you want them to open is impossible. I could try to explain it, but the gif below will show it best (I realize it's upside-down from what you want but the concept still applies).



If you tried to do this setup in the real world, the flaps would be locked in place and unable to move, as in the gif you can see that as soon as the flaps move they intersect with the walls of the bottle.

The solution to this will depend on your end goals. If you need the flaps to be visible, the only solution that I can think of would be to move the hinge to the middle of the bottle so that the flaps would fold up and meet in the middle. If you just want to keep two fluids separate and have them mix when the bottom one is forced up, there is probably a better solution for that, but I would ask a new question if that is your goal.

A couple of other things that I see that would also cause problems, even with a proper setup, are that the flaps start out partially inside the walls of the bottle. This will always break a simulation as it's a physically impossible condition. The second is that the bottle collision type is set to Convex Hull, which isn't the best for shapes with large convex areas. A better collision type would be Mesh, as it is the most accurate.

However, these are in addition to the main problem, and likely won't help unless the entire system is redesigned.